What is the integral of (sin(x))/((1-cos(x))^3) ?

The integral of (sin(x))/((1-cos(x))^3) is -1/(2(1-cos(x))^2)+C

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integral of (sin(x))/((1-cos(x))^3)

\int \frac{sin ( x )}{( 1 - cos ( x ) ) ^{3}} d x

- \frac{1}{2 ( 1 - cos ( x ) ) ^{2}} + C

Solution steps

\int \frac{sin ( x )}{( 1 - cos ( x ) ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = 1 - cos (x)

= - \frac{1}{2 ( 1 - cos ( x ) ) ^{2}}

Add a constant to the solution

= - \frac{1}{2 ( 1 - cos ( x ) ) ^{2}} + C

\frac{\partial}{\partial x} (3 x^{2} y - x + 2 y^{3})

2 x^{3} - 4 x^{2}

\int cos (4 x) cos (8 x) d x

\frac{d}{d x} (\frac{6}{3 x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x})

(y^{2} - x^{2}) d x + (- 2 x y) d y = 0

What is the integral of (sin(x))/((1-cos(x))^3) ?
The integral of (sin(x))/((1-cos(x))^3) is -1/(2(1-cos(x))^2)+C